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A charge Q is distributed over three con...

A charge Q is distributed over three concentric spherical shells of radii a, b, c (a`lt` b `lt` c) such that their surface charge densities are equal to one another.
The total potential at a point at distance r from their common centre, where r`lt`a, would be :

A

`(Q)/(12piepsilon_(0))(ab+bc+ca)/(abc)`

B

`(Q)/(4piepsilon_(0)(a+b+c))`

C

`(Q(a+b+c))/(4piepsilon_(0)(a^(2)+b^(2)+c^(2)))`

D

`(Q)/(4piepsilon_(0))((a^(2)+b^(2)+c^(2)))/((a^(3)+b^(3)+c^(3)))`

Text Solution

Verified by Experts

The correct Answer is:
C
`(q_(1))/(a^(2))=(q^(2))/(b^(2))=(q_(3))/(c^(2))` = constant
`q_(1)+q_(2)+q_(3)=0`
`q_(1)=(a^(2)(Q))/(a^(2)+b^(2)+c^(2))`
`q_(2)=(b^(2)(Q))/(a^(2)+b^(2)+c^(2))`
`q_(3)=(c^(2)(Q))/(a^(2)+b^(2)+c^(2))`
`V=(Kq_(1))/(a)+(Kq_(2))/(b)+(Kq_(3))/(c)`
`V=(1)/(4piepsilon_(0))[Q]((a+b+c)/(a^(2)+b^(2)+c^(2)))`.
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